Credit Derivatives with Multiple Debt Issues

Abstract

We extend the class of structural models of credit derivatives by allowing for multiple debt issues. Since firms default on all of their obligations, total debt is instrumental in the likelihood of default and therefore in credit derivatives valuation. We use a mono-factor interest rate model where the exponential default frontier is based on total debt and is made coherent with observed bond prices. Analytical formulae are derived for credit default swaps, total return swaps (both fixed-for-fixed and fixed-for-floating), and credit risk options. Simulations document that credit derivatives prices are affected in a non-trivial way by terms of debt other than those of the reference obligation.

Keywords: credit derivatives, credit risk, structural model

JEL Classification: G12, G13